Quasilinear hyperbolic equations with hysteresis

Augusto Visintin

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Limit behaviour of thin insulating layers around multiconnected domains

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Quasilinear hyperbolic equations with hysteresis

Augusto Visintin (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Hysteresis operators are illustrated, and a weak formulation is studied for an initial- and boundary-value problem associated to the equation $(\partial^{2} / \partial t^{2}) [u + F (u)] + A u = f$ ; here $F$ is a (possibly discontinuous) hysteresis operator, $A$ is a second order elliptic operator, $f$ is a known function. Problems of this sort arise in plasticity, ferromagnetism, ferroelectricity, and so on. In particular an existence result is outlined.

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